Australia's king-maker Greens party has flexed its new found political muscle in a failed bid to topple the government's choice of senate president.

The tussle over the senate's top job exposed tensions between Australia's ruling Labour Party and the left-wing Greens whose support is crucial to the survival of prime minister Julia Gillard's fragile government.

The result of senate elections in August last year came into effect on Friday when the Greens' representation grew from five to nine senators.

The Greens now hold the balance of power in the Senate, with sufficient numbers to pass the minority Labour Party government's legislative agenda through the upper chamber against the wishes of the opposition coalition.

At the first session of the new senate, the Greens attempted to break the tradition of the government choosing the Senate president by nominating the party's own candidate.

However, Labour's candidate senator John Hogg, who was president during the party's last three-year term in government, defeated the Greens' senator Scott Ludlam by 62 votes to nine. Mr Ludlam apparently failed to attract a single vote from outside his party.

Greens' leader senator Bob Brown said the vote would be part of a pattern in the new Senate in which centre-left Labour and the conservative opposition Liberal Party-led coalition join forces against a progressive agenda.

Neither Labour nor the opposition command a majority of Senate seats.

"On many, many issues, the two big parties will be getting together to use their numbers against the innovation of this very progressive and growing force in politics," Mr Brown told the Senate.

"We now have the Greens in the position of being the third party in this chamber, and we do intend to take a vigorous role in offering alternatives," he added.